Related papers: Compact quantum stabilizer subgroups
We study the stability of certain spectra under some algebraic conditions weaker than the commutativity and we generalize many known commutative perturbation results.
We introduce the notion of integrable modules over $\imath$quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is…
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
In this work, we study the Codeword Stabilized Quantum Codes (CWS codes) a generalization of the stabilizers quantum codes using a new approach, the algebraic structure of modules, a generalization of linear spaces. We show then a new…
In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…
We study the concept of co-amenability for a compact quantum group. Several conditions are derived that are shown to be equivalent to it. Some consequences of co-amenability that we obtain are faithfulness of the Haar integral and automatic…
The generalization of multiplicative unitary notion from compact quantum groups to compact quantum semigroups is considered. We show why the same construction doesn't work in this case by giving examples of C*-algebras with non-trivial…
Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…
We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We then investigate examples, proving in particular the Property of Rapid Decay for unimodular free…
In this paper we classify reflection subgroups of Euclidean Coxeter groups.
This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…
Some recent developments in the theory of quantum spin systems are reviewed.
We give an overview of moduli stabilization in compactifications of string theory. We summarize current methods for construction and analysis of vacua with stabilized moduli, and we describe applications to cosmology and particle physics.…
The aim of this paper is to provide an overview of the results about classification of quantum groups that were obtained in arXiv:1303.4046 [math.QA] and arXiv:1502.00403 [math.QA].
We show that a natural notion of irreducibility implies connectedness in the Compact Quantum Group setting. We also investigate the converse implication and show it is related to Kaplansky's conjectures on group algebras.
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…